In quick succession this week, three small groups of people, from Syria, Pakistan and Afghanistan, have reportedly tried to enter the United States through the border with Mexico, fanning fears that violent jihadists could make their way into the country.

Federal officials say there are no indications that any of the migrants had radical history or intentions, and one of the groups did not try to sneak across the border but surrendered voluntarily. But the incidents come in a politically charged atmosphere, less than a week after the deadly Paris attacks by the Islamic State, as many Republican officials and some Democrats around the country argue that militants could be hiding among people fleeing the Syrian civil war and other conflicts.

Most governors have vowed to try to block President Obama’s plan to settle 10,000 Syrian refugees in the United States, and the House of Representatives voted overwhelmingly on Thursday to make it much harder to admit them into the country.

Advocates of stricter border control, including many border-region officials, have long cited the possibility that violent radicals could slip into the stream of Latin Americans crossing the United States’ southern border. That has not been a common route for migrants from the Middle East, but any indication that it is becoming one could ratchet up security concerns.

“My fear — and what should be the fear of all Americans — is that terrorists are using well-established smuggling routes through Central America, through Mexico, and positioning themselves to come across the border,” said Sheriff Paul Babeu of Pinal County, Ariz., which straddles one of the region’s major corridors for smuggling people and drugs into the country.

On Thursday, United States Customs and Border Protection confirmed that Border Patrol agents had apprehended five Pakistanis and one Afghan on Monday, after they illegally crossed the border south of Tucson. The men were caught, along with two smugglers, near Sonoita, Ariz., a small town in Santa Cruz County near a national forest, and were being held in federal custody.

“As a standard procedure, agents processed the six individuals and checked their identities against numerous law enforcement and national security related databases,” the agency said in a statement. “Records checks revealed no derogatory information about the individuals.”

Federal officials said the group is still under investigation.

The terrain where they were caught is mountainous and rocky, and much of the illegal trade through it is run by the Sinaloa drug cartel, which dominates the adjoining region of Mexico. If the cartel is doing business with terrorists, “that’s a dangerous alliance,” said Sheriff Tony Estrada of Santa Cruz County, but he questioned how much better protected the border could be.

“We have thousands of federal, county and local law enforcement agents here,” he said. “To say that the border must be sealed, that no one or nothing should come through, is absurd, impossible.”

On Tuesday, eight Syrians — two men, two women and four children, all from two families — presented themselves to the authorities at the border in Laredo, Tex., and asked for refuge in the United States, Immigration and Customs Enforcement said. Officials said the Syrians, who were sent to detention centers, will go through regular screening and immigration court procedures to see if they qualify for asylum, a process that could take years. The officials would not provide more information, citing “privacy issues.”

Some news reports erroneously said the group had been “caught” at the border, language that was repeated by critics of American immigration policy, including Donald J. Trump, the presidential candidate who has made border enforcement a central issue in the campaign.

Mr. Trump took to Twitter on Thursday, posting messages in which he asked whether the Syrians were part of the Islamic State, and added: “I told you so. WE NEED A BIG & BEAUTIFUL WALL!” Gov. Greg Abbott of Texas, a Republican who has been one of the most vocal opponents of the president’s refugee policy, cited the border episode when he said on Twitter, “This is why Texas is vigilant about Syrian refugees.”

Gov. Doug Ducey of Arizona, also a Republican, said he was pleased that the people had been apprehended, but added, “more vigilance is needed at all levels.”

Also this week, officials in Honduras arrested five Syrian men who had arrived at the airport in Tegucigalpa with forged or stolen Greek passports and who they said intended to head overland to the United States. The Honduran authorities said the men had traveled a circuitous route through multiple countries, mostly in Latin America.

Appearing Wednesday on Fox News, Mr. Abbott said, “It was discovered by Honduran officials that Syrians were coming through Honduras on their way to the United States to wreak terroristic activity.” But American and Honduran officials said they had seen no evidence that the men were terrorists.

Muslim nations have accounted for a relatively small part of illegal migration to the United States. Out of some 700,000 migrants apprehended each year, according to the Department of Homeland Security, no more than a few hundred come from Syria, Pakistan or Afghanistan.

Correction:Nov. 21, 2015

An article on Friday about efforts by three small groups of people from Syria, Pakistan and Afghanistan to enter the United States through Mexico misstated, in some editions, the surname of an Arizona sheriff who commented on the border crossings. He is Paul Babeu, not Pabeu.

A version of this article appears in print on , Section A, Page 10 of the New York edition with the headline: Migrants’ Attempts to Enter U.S. via Mexico Stoke Fears About Jihadists. Order Reprints | Today’s Paper | Subscribe